Generically speaking: pixel = dot = point. They are different physical elements, depending on the medium you're working in. On computer monitors, pixels matter. In printing, dots are what count. Points are more generic and could refer to pixels or dots. The terms are commonly interchanged and often confused.
"Resolution" is the total number of [pixels, points or dots] wide, by total number of [pixels, points or dots] high. So a printer could have a resolution of 1200x1200 dots per inch, while a monitor could have a resolution of 1280x1024.
DPI and PPI are simply ratios. DPI is "dots per inch," PPI is "points per inch" or "pixels per inch." Those ratios increase and decrease based on the resolution (width x height, in pixels) and size (in inches) of a given medium.
To calculate the DPI, you need to determine the actual physical widths and heights of the medium. A common example is the Apple iPhone 4 screen:
Physical Width = 1.94 inches
Physical Height = 2.91 inches
Width (in pixels) = 640
Height (in pixels) = 960
The assumption is that all pixels, dots, or points occupy a square space. Therefore, the simple equation to determine PPI / DPI is to divide pixel height by physical height, yielding roughly 329 DPI.
This information helps to answer your question. Windows does not have any idea what the DPI of your display is, because it has no concept of what the physical dimensions of the display are. You can buy 20" monitors with 1920x1080 resolution, as well as 70" monitors with the same 1920x1080 resolution. Both have signficantly different DPI's, yet Windows has no idea and nothing to do with it.
While Windows offers the option of increasing or decreasing the DPI, all it will really do is adjust system font sizes and default icon / UI sizes of things. Many other apps, graphics, websites and emails will actually get very poorly distorted if you make changes to the DPI settings.
Apple Mac OS (especially iOS) has significantly better support for DPI, and knows, based on the devices it is installed on, which DPI setting to use.
They can't, some parameters have been reported incorrectly. You can verify this yourself as follows.
There is a convenient pixel density calculator at this website. The calculation is trivial (from wikipedia)
Using this formula and/or the online calculator shows that for the X250 to have a ppi of 183 with a resolution of 1920x1080 it would need to be a 12" screen, not a 12.5" screen.
Using the value of 12" instead of 12.5" comes out to almost exactly 183 ppi while 12.5" comes to 176.
So either the manufacturer has redefined ppi, or they are not reporting the resolution or screen size accurately.
Best Answer
I am assuming you mean the current DPI is 64ppi x 64 ppi. You want GIMP to add pixels to the 1024x768 image without changing the size in inches. The only way I know to do this is in two steps, both of which use Image | Scale Image.
In Image | Scale Image, set Interpolation to None and change the X and Y resolution. You will see that the Image Size in pixels doesn't change. Hit Scale, and the image will have the new resolution.
Go back into Image | Scale Image. Set Interpolation to Cubic. This time, change the Image Size to be what you want in inches or cm. GIMP will compute the resulting pixel resolution and resample the image.
This way you don't have to manually convert between inches, dpi, and pixels. Hope this helps!